On stability of nonlinear difference equations and some of their applications

M.M. Aripov; D. Utebaev; B.D. Utebaev; R.Sh. Yarlashov

doi:10.31489/2024m3/13-25

Authors

M.M. Aripov National University of Uzbekistan named after Mirzo Ulugbek, Tashkent, Uzbekistan https://orcid.org/0000-0001-5207-8852
D. Utebaev Karakalpak State University named after Berdakh, Nukus, Uzbekistan https://orcid.org/0000-0003-1252-6563
B.D. Utebaev Karakalpak State University named after Berdakh, Nukus, Uzbekistan; Karakalpak branch of the Institute of Mathematics named after V.I. Romanovsky of the Academy of Sciences of the Republic of Uzbekistan, Nukus, Uzbekistan https://orcid.org/0009-0006-8168-9904
R.Sh. Yarlashov Karakalpak State University named after Berdakh, Nukus, Uzbekistan https://orcid.org/0000-0003-4842-2205

DOI:

https://doi.org/10.31489/2024m3/13-25

Keywords:

nonlinear difference equations, difference schemes, a priori estimates, stability

Abstract

The issues of stability in solving nonlinear difference equations were considered. Based on a generalized difference analog of the well-known Bihari lemma, stability conditions for a trivial solution based on initial data were obtained, and an a priori estimate of stability under permanent disturbances was determined. The results were used to study the stability of solving explicit and implicit difference schemes approximating nonlinear parabolic equations.

On stability of nonlinear difference equations and some of their applications

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